Ph.D.'s in Number Theory at the University of Michigan

The following is a list of the Ph.D. degrees awarded in number theory, including the dissertation title, the thesis advisor, and (when known) the first post-Ph.D. place of employment.

2018

Corey Everlove
(Lagarias) University of Michigan

Brandon Carter
Jochnowitz congruences at residual primes
(Prasanna) Google

Charlotte Chan
Period identities of CM forms on quaternion algebras
(Prasanna) Princeton University

2017

Daniel Barter
Some remarks about the interaction between quantum algebra and representation stability
(Snowden) Australian National University

Gene Kopp
Indefinite theta functions and zeta functions
(Lagarias) University of Bristol

2016

Adam Kaye
Arithmetic of the Asai L-function for Hilbert modular forms
(Prasanna) Goldman Sachs

Suchandan Pal
An explicit Jacquet–Langlands correspondence
(Prasanna) Mavenir

2015

Ariel Shnidman
Heights of generalized Heegner cycles
(Prasanna) Boston College

2014

Harry Altman
Integer complexity, addition chains, and well-ordering
(Lagarias)

Sijun Liu
Functional equations involving Laurent polynomials and meromorphic functions, with applications to dynamics and Diophantine equations
(Zieve) Oracle

Hieu Ngo
Generalizations of the Lerch zeta functions
(Lagarias) Texas A&M University at Qatar

2013

Hunter Brooks
Generalized Heegner cycles, Shimura curves, and special values of p-adic L-functions
(Prasanna) EPFL - Switzerland

Alex Mueller
Applications of generalized Fermat varieties to zeta functions of Artin-Schreier curves
(Zieve) Less Annoying CRM

Julian Rosen
The arithmetic of multiple harmonic sums
(Lagarias) Waterloo

Zach Scherr
Rational polynomial Pell equations
(Zieve) Penn

2011

Ben Weiss
Diophantine equations with two separated variables
(Lagarias/Zieve) Technion

2010

Johnson Jia
The arithmetic of the Yoshida lift
(Skinner/DeBacker) University of British Columbia

Brian Wyman
Polynomial decomposition over rings
(Zieve) PNYLAB LLC

2009

Jonathan Bober
Integer ratios of factorials, hypergeometric series, and related step functions
(Lagarias) Institute for Advanced Study

Ellen Eischen
p-adic differential operators on automorphic forms and applications
(Skinner/Ramsey) Northwestern University

Leo Goldmakher
Multiplicative mimicry and improvements of the Polya-Vinogradov theorem
(Soundararajan/Lagarias) University of Toronto

Hester Graves
On Euclidean ideal classes
(Ramsey) Queen's University

Wansu Kim
Galois deformation theory for norm fields and its arithmetic applications
(Conrad/DeBacker) Imperial College

2008

Craig Spencer
Analytic methods for Diophantine problems
(Wooley/Lewis) Institute for Advanced Study

2007

Mahesh Agarwal
p-Adic L-functions for GSp(4) x GL(2)
(Skinner) McMaster University

Bryden Cais
Compatabilities, correspondences, and integral structure in p-adic cohomology
(Conrad) McGill University

Rizwanur Khan
Non-vanishing of the symmetric square L-function
(Soundararajan) UCLA

Matthew Smith
On solution-free sets for simultaneous additive equations
(Wooley) University of Georgia

2006

Trevor Arnold
Anticyclotomic Iwasawa Theory for Modular Forms
(Skinner) University of Washington

Krzysztof Klosin
Congruences among automorphic forms on the unitary group U(2,2)
(Skinner) University of Utah

2005

Peng Gao
n-level densities of zeros of quadratic Dirichlet L-functions
(Montgomery/Soundararajan) AIM/Montreal

Sreekar Shastry
J_1(n) has connected fibers
(Conrad) Tata Institute (Bombay)

2004

Tobias Berger
Eisenstein ideal for imaginary quadratic fields
(Skinner) Cambridge University

Jim Brown
Sato-Kurokawa lifts and L-values
(Skinner) Ohio State University

Tong Liu
Potentially good reduction of Barsotti-Tate groups
(Conrad) University of Pennsylvania

2003

Mihran Papikian
Optimal elliptic curves and degree conjecture over function fields
(Conrad) Stanford University

2002

Tsz Ho Chan
Pair correlation and distribution of prime numbers
(Montgomery) Case Western Reserve University

2000

Michael Knapp
Forms in many variables over p-adic fields
(Wooley) University of Rochester

Joseph Palen
Bounds for class members of cyclotomic function fields
(Lewis)

1999

Eric Freeman
Quadratic and cubic diophantine inequalities
(Wooley)

Scott Parsell
Exponential sums and diophantine problems
(Wooley)

Victor Scharaschkin
Local-global problems and the Brauer-Manin obstruction
(Milne)

1998

Matt DeLong
Relating elliptic curves to three-ranks of quadratic number fields
(Milne)

Pierre Giguere
On the conjecture of Langlands and Rapoport
(Milne)

Tony Vazzana
4-ranks of K_2 of rings of integers in quadratic number fields
(Milne)

Joel Wisdom
On the representations of numbers as sums of powers
(Wooley)

1997

Greg Martin
The distribution of prime primitive roots and dense Egyptian fractions
(Montgomery/Wooley)

1996

Stefan Treatman
Euclidean systems
(Milne)

1995

Morley Davidson
Waring's problem in number fields
(Wooley)

1994

Mary Armon
Sums of quadratic characters
(Montgomery)

1993

Matthias Pfau
The reduction of connected Shimura varieties at primes of good reduction
(Milne)

David Santos
Sets of monotonicity for the Riemann zeta-functions
(Montgomery)

Wafa Wei
Weil numbers and generating large field extensions
(Milne)

1992

Kent Boklan
The asymptotic formula in Waring's problem
(Montgomery)

Hemar Godinho
A pair of additive quartic forms
(Lewis)

1990

John Rickert
Simultaneous rational approximations and related Diophantine equations
(Masser)

1989

Daniel Kornhauser
Bounds for the smallest integer solution of general quadratic equations
(Masser)

Jungseob Lee
On the constant in the Turan-Kubilius inequality
(Montgomery)

Thomas Martin
Minimal theta functions
(Montgomery)

Noel Wass
Algebraic independance of the values at algebraic points of a class of functions considered by Mahler
(Masser)

1987

David Folk
On the genus of normal closures of rational function field extensions
(Lewis)

Fred Schultheis
Explicit reciprocity laws in algebraic function fields
(Lewis/P.Blass)

1986

Capi Corrales-Rodriganez
Nevanlinna theory in the p-adic plane
(Lewis)

1985

Jerome Solinas
A theorem of metric Diophantine approximation and estimates for sums involving binary digits
(Montgomery)

1984

Todd Cochrane
Small solutions of congruences
(Lewis)

1983

Russell Lyons
A characterization of measures whose Fourier-Stiltjes transforms vanish at infinity
(Montgomery/Shields)

1982

William Hawkins, Jr.
The etale cohomology of certain p-torsion sheaves
(Milne)

Ali Özlük
Pair correlation of zeros of Dirichlet L-functions
(Montgomery)

1980

Brian Conrey
Zeros of derivatives of Riemann's XI function on the critical line
(Montgomery)

David Leep
Common value properties of quadratic forms
(Lewis)

William Monach
Numerical investigation of several problems in number theory
(Montgomery)

Michael Robinson
Topics in the theory of irrational numbers
(Montgomery)

1979

Steve Gonek
Analytic properties of zeta and L-functions
(Montgomery)

William Miller
Transcendence measures for values of analytic solutions to certain functional equations
(Montgomery)

Patrick Morton
The 2-classgroup of a quadratic number field and the Pell equation X^2- delta Y^2 = -1
(Lewis)

1977

Andrew Baily
On the density of discriminants of quartic fields
(Lewis)

Piotr Blass
Zariski surfaces
(Milne/Hochster)

Sidney Graham
Applications of sieve methods
(Montgomery)

Gerry Myerson
Equations in finite fields
(Lewis/Ullman)

1976

Michal Bester
Local flat duality of abelian varieties
(Milne)

John Driggs
Approximations to solutions over henselian rings
(Lewis)

Stephen Ricci
Local distribution of primes
(Montgomery)

1975

Ralph Toliver
Bounds for solutions of two simultaneous additive equations of odd degree
(Lewis)

1973

Fern Ellison
Three diagonal quadratic-forms
(Lewis)

Henry Thomas, Jr.
A numerical approach to Waring's problem for fourth powers
(Lewis)

1972

Maurice Craig
Irregular discriminants
(Lewis)

1971

Erik Lippa
Hecke operators for modular forms of genus R
(Lewis)

Catherine Stahl
Systems of additive equations over algebraic number fields
(Lewis)

1969

Robert Kubota
Waring's problem in FQ[X]
(Lewis)

Susan Schuur
Systems of quadratic forms over local fields
(Lewis)

1967

Michael Fried
Value sets of polynomials
(Lewis)

Charles Ryavec
Problems in diophantine analysis
(Lewis)

Gretchen Wagner
Module decompositions of ideals in Dedekind domains
(Lewis)

1966

Charles MacCluer
On exceptional polynomials
(Lewis)

1965

Underwood Dudley
The distribution modulo 1 of oscillating functions
(LeVeque)

Joseph Heisler
Diophantine problems for matrix rings, rings of functions, and other rings
(Lewis)

1964

Elizabeth Grobe
Some `p'-adic and `g'-adic versions of Roth's theorem
(LeVeque)

1963

Thomas Walker, Jr.
Two metric theorems in Diophantine approximation
(LeVeque)

1962

Klaus Guting
About algebraic and transcendental numbers
(LeVeque)

1950

Donald J. Lewis
Cubic homogeneous polynomials over a p-adic number field
(Brauer)